The invention refers to a cutting machine comprising a cutting arm being swivellable around a horizontal axis and a vertical axis and carrying on its free end the cutting tool, the horizontal swivelling axis of the cutting arm being displaceable relative to the frame of the cutting machine. By displaceably arranging the horizontal swivelling axis, the operating range of the cutting tool is increased. From the DE-OS No. 27 20 380 there has become known a cutting machine in which the turntable of the cutting arm support is shiftably supported on the cutting machine by means of a guiding sliding carriage. From the DE-OS No. 26 56 703 there has become known a cutting machine in which the horizontal swivelling axis is shiftably supported on the cutting machine by means of a guiding sliding carriage, the console of the sliding carriage being supported on the machine frame for being swivellable in the vertical plane and for being turnable around a vertical axis. In both cases there are required expensive guiding sliding carriages which are subject to a heavy wear on account of the dust generation. Furthermore, the operating range of the cutting tool is only insufficiently increased by the guiding sliding carriage.